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3. Listeners Paradise, a used CD store has daily fixed costs of $437 per day and...

3. Listeners Paradise, a used CD store has daily fixed costs of $437 per day and 40 CDs cost $557 to produce. The CD’s sell for $12.50 each.

(a) Find an equation for the total daily cost, C(x)

(b) Find an equation for the total daily revenue, R(x).

(c) Find an equation for the profit function, P(x).

(d) Find the number of CD’s that must be sold daily in order to break even.

math   Statistics-And-Probability   
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Answer #1

3a) Fixed cost = $437

So, C = 437+b*x

C(40) = 557

557 = 437 + b*40

557 - 437 = 40b

b = 120/40 = 3

So, cost function: C(x) = 437 + 3x

b) Revenue function: R(x) = 12.5x

c) Profit function: P(x) = R(x) - C(x) = 12.5x - (437 + 3x) = 9.5x - 437

P(x) = 9.5x - 437

d) For breakeven P(x) = 0

9.5x - 437 = 0

9.5x = 437

x = 437/9.5

x = 46

So, in order to breakeven Listerner Paradise should sell 46 CDs daily.

Please comment if any doubt. thank you.

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